A computer virus is spread by way of e - mail messages, and is planted in 3 mach

Question

A computer virus is spread by way of e - mail messages, and is planted in 3 machines the first day. Each day, each infected machine from the day before infects 5 new machines. Let a_n be the total number of machines that are infected (have this virus) on the nth day. (a). Write a recurrence for a_n. Do not forget the complete set of initial conditions! (You do not have to solve the recurrence.) (b). Now suppose that on the second day a software solution is found to counteract the virus, and one machine is cleaned on this (the second) day. End) day thereafter, twice as many machines are cleaned as were cleaned the day before. Write a recurrence for Do not forget the complete set of initial conditions! (You do not have to solve the recurrence.)

Explanation / Answer

Solution:

initial condition a0= 3 (3 machine infected on the first day),

And if those 3 infect 5 each, i,e, a1= 5*3=15. (2nd day)

And if those 15 infect 5 each,

a2=5*3*3 = 45. (3rd day)

so on

A recurrence relation for total number of machine that are infected on the n th day an wil be

an=5.an-1

b)

a0= 3 (3 machine infected on the first day),

a1= 1 (1 machine is cleaned on the second day)

Recurrence relation will be an= 5*an-1 - 2 n-2 when n >= 2

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